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Homework Statement
A circuit has an inductor of self inductance 5L connected in series with a resistor of resistance R and a cell of emf E. After a long time, a new inductor of inductance 4L is suddenly connected in series to the arrangement, keeping the rest of the arrangement intact. What is the current in the circuit immediately, after the new inductor has been introduced?
Homework Equations

The Attempt at a Solution
I am not really able to figure out how to approach the problem. After a long time, in the initial arrangement, the current in the circuit will just be E/R. The moment i introduce the the 4L inductor, it will tend to provide infinite resistance to the circuit but at the same time it cant stop the flow of current as the 5L inductor wont allow the current through it to drop to zero immediately. So how will the current flow at the immediate instant. Mathematically too i haven't found anything that can really help to get through.
Please help!!!
The answer given is 5E/9R